The area of a circle is given by $\(\pi r^2\)$, where $r$ is the radius of the circle. If the area of the larger circle is $\(100 \pi\)$, this makes $\(r^2=100\)$, which makes the radius of the large circle 10 .

There are a few things to remember about chords like $\(V X\)$. Any radius that passes through a chord serves as a perpendicular bisector of the chord, meaning that we can form a right triangle out of any radius of the large circle, the radius of a small circle, and half of the length of $\(V X\)$.



Setting $r$ as the radius of the small circle and using the Pythagorean theorem, we have:

$$
\(\begin{aligned}
r^2+62 & =100 \\
r^2+36 & =100 \\
r^2 & =64 \\
r & =8
\end{aligned}\)
$$


The radius of the small circle is 8 .